factor(Module) -- factor a ZZ-module

Synopsis

Function: factor
Usage:

factor M
Inputs:
- M, a module
Outputs:
- a symbolic expression describing the decomposition of M into a direct sum of principal modules

Description

The ring of M must be ZZ.

In the following example we construct a module with a known (but disguised) factorization.

i1 : f = random(ZZ^6, ZZ^4)

o1 = | 8 3 8 6 |
     | 1 7 5 8 |
     | 3 8 2 6 |
     | 7 8 3 9 |
     | 8 5 6 3 |
     | 3 7 3 7 |

              6       4
o1 : Matrix ZZ  <-- ZZ

i2 : M = subquotient ( f * diagonalMatrix{2,3,8,21}, f * diagonalMatrix{2*11,3*5*13,0,21*5} )

o2 = subquotient (| 16 9  64 126 |, | 176 585  0 630 |)
                  | 2  21 40 168 |  | 22  1365 0 840 |
                  | 6  24 16 126 |  | 66  1560 0 630 |
                  | 14 24 24 189 |  | 154 1560 0 945 |
                  | 16 15 48 63  |  | 176 975  0 315 |
                  | 6  21 24 147 |  | 66  1365 0 735 |

                                 6
o2 : ZZ-module, subquotient of ZZ

i3 : factor M

          ZZ   ZZ    ZZ
o3 = ZZ + -- + -- + ----
           5   11   5*13

o3 : Expression of class Sum

Ways to use this method: